Dual-phase carbide-boride ceramics in different vanadium-Me (Me = Cr, Hf, Ti, and Zr) binary systems were synthesized by boro/carbothermal reduction under stoichiometric and carbon-deficient conditions and densified by spark plasma sintering. Thermodynamic analysis was used to evaluate the influence of composition on the phase stability and metal segregation between phases, along with the resulting effects on microstructure and hardness. Pairing vanadium with Group IV elements (Hf, Ti, and Zr) consistently formed one boride and one carbide phase, while the Cr-V system formed a monoboride phase and a carbon-deficient carbide. Metal segregation trends depended on composition. Vanadium preferentially segregated to the carbide phase in the Ti-V and Cr-V systems, while it was enriched in the boride phase in Hf-V and Zr-V systems. Hardness measurements showed a higher hardness for the Ti-V sub-stoichiometric system, reaching 27.7 +/- 0.9 GPa at 9.8 N, while the Cr-V sub-stoichiometric system presented the lowest hardness at 18.8 +/- 0.3 GPa at the same load. Notably, in the Zr-V system, thermodynamic predictions based solely on standard Gibbs energy deviated from experimental observations. However, when combined with first-principles calculations that accounted for non-stoichiometry in vanadium carbide, the predictions aligned more closely with experimental observations, qualitatively indicating a preference for vanadium segregation to the boride phase and zirconium to the carbide phase. These results suggest that elemental distribution between phases results from complex interactions beyond simple Gibbs free energy minimization, especially in systems like Zr-V with strong carbide-to-boride ratio dependence. The optimized systems were characterized with nominal compositions of (Ti0.61,V0.39)B2-(Ti0.39,V0.61)C0.9, (Hf0.12,V0.88)B2-(Hf0.88,V0.12)C0.9, (Zr0.29,V0.71)B2-(Ti0.71,V0.29)C0.9 and (Cr0.60,V0.40)B-(Cr0.40,V0.60)C0.8. Their thermodynamic interactions provided insights into metal segregation in dual-phase ceramics, demonstrating its strong composition dependence.

We present the Plan for Robust and Accurate Potentials (PRAPs), a software package for training and using moment tensor potentials (MTPs) in concert with the Machine Learned Interatomic Potentials (MLIP) software package. PRAPs provides an automated workflow to train MTPs using active learning procedures, and a variety of utilities to ease and improve workflows when utilizing the MLIP software. PRAPs was originally developed in the context of crystal structure prediction, in which one calculates convex hulls and predicts low energy metastable and thermodynamically stable structures, but the potentials PRAPs develops are not limited to such applications. PRAPs produces two potentials, one capable of rough estimates of the energies, forces and stresses of almost any chemical structure in the specified compositional space – the Robust Potential – and a second potential intended to provide more accurate descriptions of ground state and metastable structures – the Accurate Potential. We also present a Python library, mliputils, designed to assist users in working with the chemical structural files used by the MLIP package.

Spinodal decomposition, a key mechanism to microstructure formation in materials, has long posed challenges for predictive modeling, due to the need for parameter-free approaches that accurately capture local energy landscapes. In this work, we propose an approach to predict spinodal behavior by introducing a disorder viscosity correction to bulk free energies computed from finite, small, representative cells. We approximate the energy penalty required to transition into a disordered state to enable the stabilization of locally concave bulk free energy regions — essential for interface formation — while suppressing long-range concentration fluctuations. This approximation circumvents the complexity of full ab initio parameterization of interfacial properties and is well-suited for high-throughput and machine-learning frameworks. Our approach captures the necessary physics underpinning spinodal kinetics, offering a scalable route to predict spinodal regions in compositionally complex and high-entropy materials.

In the study of complex systems, the intricate interdependence among individual components leads to emergent properties that cannot be solely attributed to the properties of the components themselves. This principle is central to compositionally complex materials (CCMs), where interactions between different elements introduced into the structure result in unprecedented material properties. The emergence of high-entropy materials (HEMs) in 2004 further increased complexity by introducing high configurational entropy (S _config ), which can contribute to stabilizing single-phase solid solutions by counterbalancing enthalpic driving forces for phase separation. HEMs and CCMs represent an emerging family of materials where multiple principal elements occupy equivalent crystallographic sites. This atomic architecture gives rise to extraordinary properties such as tailorable electronic structures, lattice distortion effects, and synergistic interactions, with their vast combinatorial design space enabling the tuning of these effects across a wide range of compositions. Although the field is still in its infancy, early discoveries highlight their disruptive potential, particularly in energy technologies where robustness and durability are critical. Their exceptional thermal stability, corrosion resistance, and electro-chemo-mechanical durability position HEMs and CCMs as game-changers for applications demanding resilience under harsh operating conditions, such as batteries, fuel cells, and hydrogen storage systems. Beyond performance advantages, CCMs challenge traditional materials discovery frameworks. Their extensive design space makes conventional trial-and-error approaches impractical, creating an ideal platform for deploying AI-driven high-throughput computational screening, multiscale modeling, and autonomous experimental workflows. This convergence of complexity and innovation offers unprecedented opportunities to accelerate the identification of next-generation energy materials. This roadmap compiles insights from leading experts in the field of CCMs across key energy domains, including electrochemical storage, catalysis, thermoelectrics, and turbomachinery. Their contributions critically assess the current state of this material family, highlighting unresolved scientific challenges, technological barriers, and the key advancements needed to move beyond the current state-of-the-art. Special emphasis is placed on combinatorial synthesis and high-throughput approaches and their potential to trigger exponential development of this emerging family of materials. Focused on energy applications, this roadmap provides a comprehensive overview of a time-critical topic, emphasizing the need for material innovation and joint efforts from academia and industry.

The AFLOW library of crystallographic prototypes has been updated to incorporate an additional 344 entries, which now reaches 2,127 prototypes. ICSD and CCDC numbers have been added to the website alongside improvements to the user interface. New tutorials covering the basics of crystallography in the context of materials science have also been added. Lastly, we covered the current known applications of AFLOW prototype labels and materials data across research software.

Immiscibility was investigated in Group IV – Group V transition metal diboride pseudobinary systems (TiB2 – NbB2, TiB2 – TaB2, ZrB2 – NbB2, ZrB2 – TaB2, HfB2 – NbB2, and HfB2 – TaB2), revealing classic eutectic lamellar microstructures. Autocorrelation analysis of the microstructure length scales was used to validate the eutectic nature of these microstructures. These results indicate that substantial revisions are required for the pseudobinary phase diagrams of Group IV – Group V transition metal diborides available in the literature and explain several discrepancies between available thermochemical literature and reported microstructure results in these systems.

Dual-phase compositionally complex ultra-high temperature ceramics were formulated by incorporating different Groups V and VI metals such as V, Nb, Ta, Cr, Mo, or W into a base composition containing the Group IV elements, Hf, Ti, and Zr. Metal distribution was predicted using first-principles-based thermodynamics simulations and compared with experimental results. Moreover, phase stability, microstructure, and mechanical properties were evaluated for all of the ceramics. Compositions containing Cr, V, Nb, or Ta formed dual-phase ceramics containing only one boride and one carbide phase, while compositions containing Mo or W developed an additional third phase. The experimental metal distribution trends generally aligned with thermodynamic predictions, except for compositions containing V, which showed unexpected segregation behavior that was influenced by complex interactions of the coexistence of boride and carbide structures. From the dual-phase ceramics, the composition containing V exhibited the highest hardness (HV1 = 25.5 +/- 0.6 GPa) combined with smaller grain sizes (0.99 +/- 0.33 mu m for the boride and 1.15 +/- 0.31 mu m for the carbide phases). Our findings provide insights into phase formation and elemental segregation and help the design of next-generation dual-phase UHTCs with tailored properties.

Tailoring material properties often requires understanding the solidification process. Herein, we introduce the geometric descriptor Soliquidy, which numerically captures the Euclidean transport cost between the translationally disordered versus ordered states of a materials. As a testbed, we apply Soliquidy to the classification of glass-forming metal alloys. By extending and combining an experimental library of metallic thin films (glass/no-glass) with the aflow.org computational database (geometrical and energetic information of mixtures) we found that the combination of Soliquity and formation enthalpies generates an effective classifier for glass formation. Such a classifier is then used to tackle a public dataset of metallic glasses showing that the glass-agnostic assumptions of Soliquity can be useful for understanding kinetically-controlled phase transitions.

AFLOW4 is the latest iteration of the AFLOW toolkit, specifically tailored to study high-entropy disordered materials. This upgrade includes innovative features like the Soliquidy module, based on the Euclidean transport cost between disordered and ordered material states. AFLOW4 can calculate dielectric functions to understand optical and electronic properties of disordered ceramics. The newly introduced human-readable data export feature ensures the uncomplicated incorporation of AFLOW4 in diverse automated workflows. Features relevant to high-entropy research, like prototype identification, partial occupation method, convex hull calculation, and enthalpy corrections based on local atomic environments, have been improved and exhibit substantial speed-up. Together, these enhancements represent a step forward for AFLOW as a valuable tool for research of high-entropy materials.

Effective thermal management at variable and extreme temperatures face limitations for the development of novel energy and aerospace applications. Plasmonic approaches, shown to be capable of tailoring black-body emission, could be effective if materials with high-temperature and tunable plasmonic-resonance were available. Here, we report a synergy between experimental and theoretical results proving that many high-entropy transition-metal carbides, consisting of four or more metals at equal molar ratio, have plasmonic resonance at room, high (>1000C) and variable temperatures. We also found that these high-entropy carbides can be tuned and show considerable plasmonic thermal cycling stability. This paradigm-shift approach could prove quite advantageous as it facilitates the accelerated rational discovery and manufacturability of optically highly-optimized high-entropy carbides with ad-hoc properties.

The AFLOW Library of Crystallographic Prototypes has been updated to include an additional 683 entries, which now reaches 1,783 prototypes. We have also made some changes to the presentation of the entries, including a more consistent definition of the AFLOW-prototype label and a better explanation of our choice of space group when the experimental data is ambiguous. A method is presented for users to submit new prototypes for the Encyclopedia. We also include a complete index linking to all the prototypes currently in the Library.

Large-density functional theory (DFT) databases are a treasure trove of energies, forces, and stresses that can be used to train machine-learned interatomic potentials for atomistic modeling. Herein, we employ structural relaxations from the AFLOW database to train moment tensor potentials (MTPs) for four carbide systems: CHfTa, CHfZr, CMoW, and CTaTi. The resulting MTPs are used to relax ~6300 random symmetric structures, and are subsequently improved via active learning to generate robust potentials (RP) that can relax a wide variety of structures, and accurate potentials (AP) designed for the relaxation of low-energy systems. This protocol is shown to yield convex hulls that are indistinguishable from those predicted by AFLOW for the CHfTa, CHfZr, and CTaTi systems, and in the case of the CMoW system to predict thermodynamically stable structures that are not found within AFLOW, highlighting the potential of the employed protocol within crystal structure prediction. Relaxation of over three hundred (Mo1−xWx)C stoichiometry crystals first with the RP then with the AP yields formation enthalpies that are in excellent agreement with those obtained via DFT.

The Open Databases Integration for Materials Design (OPTIMADE) application programming interface (API) empowers users with holistic access to a growing federation of databases, enhancing the accessibility and discoverability of materials and chemical data. Since the first release of the OPTIMADE specification (v1.0), the API has undergone significant development, leading to the upcoming v1.2 release, and has underpinned multiple scientific studies. In this work, we highlight the latest features of the API format, accompanying software tools, and provide an update on the implementation of OPTIMADE in contributing materials databases. We end by providing several use cases that demonstrate the utility of the OPTIMADE API in materials research that continue to drive its ongoing development.

Spinodal decomposition can improve a number of essential properties in materials, especially hardness. Yet, the theoretical prediction of the onset of this phenomenon (e.g., temperature) and its microstructure (e.g., wavelength) often requires input parameters coming from costly and time-consuming experimental efforts, hindering rational materials optimization. Here, we present a procedure where such parameters are not derived from experiments. First, we calculate the spinodal temperature by modeling nucleation in the solid solution while approaching the spinode boundary. Then, we compute the spinodal wavelength self-consistently using a few reasonable approximations. Our results show remarkable agreement with experiments and, for NiRh, the calculated yield strength due to spinodal microstructures surpasses even those of Ni-based superalloys. We believe that this procedure will accelerate the exploration of the complex materials experiencing spinodal decomposition, critical for their macroscopic properties.

The need for improved functionalities in extreme environments is fuelling interest in high-entropy ceramics1-3. Except for the computational discovery of high-entropy carbides, performed with the entropy-forming-ability descriptor4, most innovation has been slowly driven by experimental means1-3. Hence, advancement in the field needs more theoretical contributions. Here we introduce disordered enthalpy-entropy descriptor (DEED), a descriptor that captures the balance between entropy gains and enthalpy costs, allowing the correct classification of functional synthesizability of multicomponent ceramics, regardless of chemistry and structure. To make our calculations possible, we have developed a convolutional algorithm that drastically reduces computational resources. Moreover, DEED guides the experimental discovery of new single-phase high-entropy carbonitrides and borides. This work, integrated into the AFLOW computational ecosystem, provides an array of potential new candidates, ripe for experimental discoveries.

Titanium carbonitride (TiCN) is an advanced, high-performance hard ceramic of great commercial importance that has been widely developed and employed. Nonetheless, it has only been in recent years that binderless titanium carbonitride bulk ceramics have been successfully fabricated using field-assisted sintering technology (FAST). However, the underlying structure-processing-property-performance relationships have yet to be fully evaluated, especially concerning indentation hardness of these materials across a broad range of loads and deformation length scales. In this work we aim to address these fundamental relationships and characterize the multiscale hardness phenomena in detail. It was found that the effects of soak temperature and time directly impacted the sintered microstructure and were reflected in the observed mechanical properties over various loads. Valuable insight into the load-dependence of hardness distributions, sensitivity/correlation with elasto-plastic parameters, and multiscale parameterization were developed using micro-/nanoindentation. Particularly, the load-dependent hardness sensitivity and resolvability demonstrate a fundamental tradeoff with respect to the manifested mechanical response influenced by the presence of underlying heterogeneities. These new insights relating the interplay of compositional/microstructural evolution with FAST processing parameters and multi -scale hardness are an important step in advancing next-generation hard ceramics.

The realization of novel technological opportunities given by computational and autonomous materials design requires efficient and effective frameworks. For more than two decades, aflow++ (Automatic-Flow Framework for Materials Discovery) has provided an interconnected collection of algorithms and workflows to address this challenge. This article contains an overview of the software and some of its most heavily-used functionalities, including algorithmic details, standards, and examples. Key thrusts are highlighted: the calculation of structural, electronic, thermodynamic, and thermomechanical properties in addition to the modeling of complex materials, such as high-entropy ceramics and bulk metallic glasses. The aflow++ software prioritizes interoperability, minimizing the number of independent parameters and tolerances. It ensures consistency of results across property sets - facilitating machine learning studies. The software also features various validation schemes, offering real-time quality assurance for data generated in a high-throughput fashion. Altogether, these considerations contribute to the development of large and reliable materials databases that can ultimately deliver future materials systems

Disordered materials are attracting considerable attention because of their enhanced properties compared to their ordered analogs, making them particularly suitable for high-temperature applications. The feasibility of incorporating these materials into new devices depends on a variety of thermophysical properties. Among them, thermal expansion is critical to device stability, especially in multi-component systems. Its calculation, however, is quite challenging for materials with substitutional disorder, hindering computational screenings. In this work, we introduce QH-POCC to leverage the local tile-expansion of disorder. This method provides an effective partial partition function to calculate thermomechanical properties of substitutionally disordered compounds in the quasi-harmonic approximation. Two systems, AuCu3 and CdMg3, the latter a candidate for long-period superstructures at low temperature, are used to validate the methodology by comparing the calculated values of the coefficient of thermal expansion and isobaric heat capacity with experiment, demonstrating that QH-POCC is a promising approach to study thermomechanical properties of disordered systems.

To enable materials databases supporting computational and experimental research, it is critical to develop platforms that both facilitate access to the data and provide the tools used to generate/analyze it - all while considering the diversity of users' experience levels and usage needs. The recently formulated FAIR principles (Findable, Accessible, Interoperable, and Reusable) establish a common framework to aid these efforts. This article describes aflow_org, a web ecosystem developed to provide FAIR - compliant access to the AFLOW databases. Graphical and programmatic retrieval methods are offered, ensuring accessibility for all experience levels and data needs. aflow_org goes beyond data-access by providing applications to important features of the AFLOW software, assisting users in their own calculations without the need to install the entire high-throughput framework. Outreach commitments to provide AFLOW tutorials and materials science education to a global and diverse audiences will also be presented.

By means of spin-resolved density functional theory calculations using both atomic orbitals and plane-wave basis codes, we study the electronic and magnetic ground state of single-layer NbSe2. We find that, for all the functionals considered, the most stable solution in this two-dimensional (2D) superconductor is the ferrimagnetic ground state with a magnetic moment of 1.09 μB at the Nb atoms and of 0.05 μB at the Se atoms pointing in the opposite direction. Our calculations show that the ferrimagnetic state precludes the development of charge density wave (CDW) order and their coexistence in the single-layer limit, unless graphene is considered as a substrate. The spin-resolved calculated density of states (DOS), a key fingerprint of the electronic and magnetic structure of a material, unambiguously reproduces the experimental DOS measured by scanning tunneling spectroscopy in single-layer NbSe2. Our work sets magnetism into play in this prototypical correlated 2D material, which is crucial to understand the formation mechanisms of 2D superconductivity and CDW order.